The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation

Author(s):

Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa

Department of Mathematical Analysis and Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.

E-mail: ksntksjm4@gmail.com

Professor Emeritus at: Hiroshima University,
Department of Mathematics, Faculty of Science,
Higashi-Hiroshima 739-8526,
Japan.

E-mail: jaros@fmph.uniba.sk

Department of Mathematics, Faculty of Education,
Kumamoto University, Kumamoto 860-8555,
Japan.

E-mail: tanigawa@educ.kumamoto-u.ac.jp
 

Abstract:

The system of nonlinear differential equations

is under consideration, where αi and βi are positive constants and pi(t) and qi(t) are continuous regularly varying functions on [a,). Two kinds of criteria are established for the existence of strongly decreasing regularly varying solutions with negative indices of (A) with precise asymptotic behavior at infinity. Fixed point techniques and basic theory of regular variation are utilized for this purpose.

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